crypto: ecrdsa - add EC-RDSA (GOST 34.10) algorithm

Add Elliptic Curve Russian Digital Signature Algorithm (GOST R
34.10-2012, RFC 7091, ISO/IEC 14888-3) is one of the Russian (and since
2018 the CIS countries) cryptographic standard algorithms (called GOST
algorithms). Only signature verification is supported, with intent to be
used in the IMA.

Summary of the changes:

* crypto/Kconfig:
  - EC-RDSA is added into Public-key cryptography section.

* crypto/Makefile:
  - ecrdsa objects are added.

* crypto/asymmetric_keys/x509_cert_parser.c:
  - Recognize EC-RDSA and Streebog OIDs.

* include/linux/oid_registry.h:
  - EC-RDSA OIDs are added to the enum. Also, a two currently not
    implemented curve OIDs are added for possible extension later (to
    not change numbering and grouping).

* crypto/ecc.c:
  - Kenneth MacKay copyright date is updated to 2014, because
    vli_mmod_slow, ecc_point_add, ecc_point_mult_shamir are based on his
    code from micro-ecc.
  - Functions needed for ecrdsa are EXPORT_SYMBOL'ed.
  - New functions:
    vli_is_negative - helper to determine sign of vli;
    vli_from_be64 - unpack big-endian array into vli (used for
      a signature);
    vli_from_le64 - unpack little-endian array into vli (used for
      a public key);
    vli_uadd, vli_usub - add/sub u64 value to/from vli (used for
      increment/decrement);
    mul_64_64 - optimized to use __int128 where appropriate, this speeds
      up point multiplication (and as a consequence signature
      verification) by the factor of 1.5-2;
    vli_umult - multiply vli by a small value (speeds up point
      multiplication by another factor of 1.5-2, depending on vli sizes);
    vli_mmod_special - module reduction for some form of Pseudo-Mersenne
      primes (used for the curves A);
    vli_mmod_special2 - module reduction for another form of
      Pseudo-Mersenne primes (used for the curves B);
    vli_mmod_barrett - module reduction using pre-computed value (used
      for the curve C);
    vli_mmod_slow - more general module reduction which is much slower
     (used when the modulus is subgroup order);
    vli_mod_mult_slow - modular multiplication;
    ecc_point_add - add two points;
    ecc_point_mult_shamir - add two points multiplied by scalars in one
      combined multiplication (this gives speed up by another factor 2 in
      compare to two separate multiplications).
    ecc_is_pubkey_valid_partial - additional samity check is added.
  - Updated vli_mmod_fast with non-strict heuristic to call optimal
      module reduction function depending on the prime value;
  - All computations for the previously defined (two NIST) curves should
    not unaffected.

* crypto/ecc.h:
  - Newly exported functions are documented.

* crypto/ecrdsa_defs.h
  - Five curves are defined.

* crypto/ecrdsa.c:
  - Signature verification is implemented.

* crypto/ecrdsa_params.asn1, crypto/ecrdsa_pub_key.asn1:
  - Templates for BER decoder for EC-RDSA parameters and public key.

Cc: linux-integrity@vger.kernel.org
Signed-off-by: Vitaly Chikunov <vt@altlinux.org>
Signed-off-by: Herbert Xu <herbert@gondor.apana.org.au>

1 files changed, 384 insertions, 8 deletions

diff --git a/crypto/ecc.c b/crypto/ecc.c
index 5f36792d143d..dfe114bc0c4a 100644
--- a/crypto/ecc.c
+++ b/crypto/ecc.c
@@ -1,6 +1,6 @@
 /*
- * Copyright (c) 2013, Kenneth MacKay
- * All rights reserved.
+ * Copyright (c) 2013, 2014 Kenneth MacKay. All rights reserved.
+ * Copyright (c) 2019 Vitaly Chikunov <vt@altlinux.org>
  *
  * Redistribution and use in source and binary forms, with or without
  * modification, are permitted provided that the following conditions are
@@ -31,6 +31,8 @@
 #include <linux/fips.h>
 #include <crypto/ecdh.h>
 #include <crypto/rng.h>
+#include <asm/unaligned.h>
+#include <linux/ratelimit.h>
 
 #include "ecc.h"
 #include "ecc_curve_defs.h"
@@ -132,6 +134,11 @@ static u64 vli_test_bit(const u64 *vli, unsigned int bit)
         return (vli[bit / 64] & ((u64)1 << (bit % 64)));
 }
 
+static bool vli_is_negative(const u64 *vli, unsigned int ndigits)
+{
+        return vli_test_bit(vli, ndigits * 64 - 1);
+}
+
 /* Counts the number of 64-bit "digits" in vli. */
 static unsigned int vli_num_digits(const u64 *vli, unsigned int ndigits)
 {
@@ -163,6 +170,27 @@ static unsigned int vli_num_bits(const u64 *vli, unsigned int ndigits)
         return ((num_digits - 1) * 64 + i);
 }
 
+/* Set dest from unaligned bit string src. */
+void vli_from_be64(u64 *dest, const void *src, unsigned int ndigits)
+{
+        int i;
+        const u64 *from = src;
+
+        for (i = 0; i < ndigits; i++)
+                dest[i] = get_unaligned_be64(&from[ndigits - 1 - i]);
+}
+EXPORT_SYMBOL(vli_from_be64);
+
+void vli_from_le64(u64 *dest, const void *src, unsigned int ndigits)
+{
+        int i;
+        const u64 *from = src;
+
+        for (i = 0; i < ndigits; i++)
+                dest[i] = get_unaligned_le64(&from[i]);
+}
+EXPORT_SYMBOL(vli_from_le64);
+
 /* Sets dest = src. */
 static void vli_set(u64 *dest, const u64 *src, unsigned int ndigits)
 {
@@ -242,6 +270,28 @@ static u64 vli_add(u64 *result, const u64 *left, const u64 *right,
         return carry;
 }
 
+/* Computes result = left + right, returning carry. Can modify in place. */
+static u64 vli_uadd(u64 *result, const u64 *left, u64 right,
+                    unsigned int ndigits)
+{
+        u64 carry = right;
+        int i;
+
+        for (i = 0; i < ndigits; i++) {
+                u64 sum;
+
+                sum = left[i] + carry;
+                if (sum != left[i])
+                        carry = (sum < left[i]);
+                else
+                        carry = !!carry;
+
+                result[i] = sum;
+        }
+
+        return carry;
+}
+
 /* Computes result = left - right, returning borrow. Can modify in place. */
 u64 vli_sub(u64 *result, const u64 *left, const u64 *right,
                    unsigned int ndigits)
@@ -263,8 +313,35 @@ u64 vli_sub(u64 *result, const u64 *left, const u64 *right,
 }
 EXPORT_SYMBOL(vli_sub);
 
+/* Computes result = left - right, returning borrow. Can modify in place. */
+static u64 vli_usub(u64 *result, const u64 *left, u64 right,
+             unsigned int ndigits)
+{
+        u64 borrow = right;
+        int i;
+
+        for (i = 0; i < ndigits; i++) {
+                u64 diff;
+
+                diff = left[i] - borrow;
+                if (diff != left[i])
+                        borrow = (diff > left[i]);
+
+                result[i] = diff;
+        }
+
+        return borrow;
+}
+
 static uint128_t mul_64_64(u64 left, u64 right)
 {
+        uint128_t result;
+#if defined(CONFIG_ARCH_SUPPORTS_INT128) && defined(__SIZEOF_INT128__)
+        unsigned __int128 m = (unsigned __int128)left * right;
+
+        result.m_low  = m;
+        result.m_high = m >> 64;
+#else
         u64 a0 = left & 0xffffffffull;
         u64 a1 = left >> 32;
         u64 b0 = right & 0xffffffffull;
@@ -273,7 +350,6 @@ static uint128_t mul_64_64(u64 left, u64 right)
         u64 m1 = a0 * b1;
         u64 m2 = a1 * b0;
         u64 m3 = a1 * b1;
-        uint128_t result;
 
         m2 += (m0 >> 32);
         m2 += m1;
@@ -284,7 +360,7 @@ static uint128_t mul_64_64(u64 left, u64 right)
 
         result.m_low = (m0 & 0xffffffffull) | (m2 << 32);
         result.m_high = m3 + (m2 >> 32);
-
+#endif
         return result;
 }
 
@@ -334,6 +410,28 @@ static void vli_mult(u64 *result, const u64 *left, const u64 *right,
         result[ndigits * 2 - 1] = r01.m_low;
 }
 
+/* Compute product = left * right, for a small right value. */
+static void vli_umult(u64 *result, const u64 *left, u32 right,
+                      unsigned int ndigits)
+{
+        uint128_t r01 = { 0 };
+        unsigned int k;
+
+        for (k = 0; k < ndigits; k++) {
+                uint128_t product;
+
+                product = mul_64_64(left[k], right);
+                r01 = add_128_128(r01, product);
+                /* no carry */
+                result[k] = r01.m_low;
+                r01.m_low = r01.m_high;
+                r01.m_high = 0;
+        }
+        result[k] = r01.m_low;
+        for (++k; k < ndigits * 2; k++)
+                result[k] = 0;
+}
+
 static void vli_square(u64 *result, const u64 *left, unsigned int ndigits)
 {
         uint128_t r01 = { 0, 0 };
@@ -406,6 +504,170 @@ static void vli_mod_sub(u64 *result, const u64 *left, const u64 *right,
                 vli_add(result, result, mod, ndigits);
 }
 
+/*
+ * Computes result = product % mod
+ * for special form moduli: p = 2^k-c, for small c (note the minus sign)
+ *
+ * References:
+ * R. Crandall, C. Pomerance. Prime Numbers: A Computational Perspective.
+ * 9 Fast Algorithms for Large-Integer Arithmetic. 9.2.3 Moduli of special form
+ * Algorithm 9.2.13 (Fast mod operation for special-form moduli).
+ */
+static void vli_mmod_special(u64 *result, const u64 *product,
+                              const u64 *mod, unsigned int ndigits)
+{
+        u64 c = -mod[0];
+        u64 t[ECC_MAX_DIGITS * 2];
+        u64 r[ECC_MAX_DIGITS * 2];
+
+        vli_set(r, product, ndigits * 2);
+        while (!vli_is_zero(r + ndigits, ndigits)) {
+                vli_umult(t, r + ndigits, c, ndigits);
+                vli_clear(r + ndigits, ndigits);
+                vli_add(r, r, t, ndigits * 2);
+        }
+        vli_set(t, mod, ndigits);
+        vli_clear(t + ndigits, ndigits);
+        while (vli_cmp(r, t, ndigits * 2) >= 0)
+                vli_sub(r, r, t, ndigits * 2);
+        vli_set(result, r, ndigits);
+}
+
+/*
+ * Computes result = product % mod
+ * for special form moduli: p = 2^{k-1}+c, for small c (note the plus sign)
+ * where k-1 does not fit into qword boundary by -1 bit (such as 255).
+
+ * References (loosely based on):
+ * A. Menezes, P. van Oorschot, S. Vanstone. Handbook of Applied Cryptography.
+ * 14.3.4 Reduction methods for moduli of special form. Algorithm 14.47.
+ * URL: http://cacr.uwaterloo.ca/hac/about/chap14.pdf
+ *
+ * H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, F. Vercauteren.
+ * Handbook of Elliptic and Hyperelliptic Curve Cryptography.
+ * Algorithm 10.25 Fast reduction for special form moduli
+ */
+static void vli_mmod_special2(u64 *result, const u64 *product,
+                               const u64 *mod, unsigned int ndigits)
+{
+        u64 c2 = mod[0] * 2;
+        u64 q[ECC_MAX_DIGITS];
+        u64 r[ECC_MAX_DIGITS * 2];
+        u64 m[ECC_MAX_DIGITS * 2]; /* expanded mod */
+        int carry; /* last bit that doesn't fit into q */
+        int i;
+
+        vli_set(m, mod, ndigits);
+        vli_clear(m + ndigits, ndigits);
+
+        vli_set(r, product, ndigits);
+        /* q and carry are top bits */
+        vli_set(q, product + ndigits, ndigits);
+        vli_clear(r + ndigits, ndigits);
+        carry = vli_is_negative(r, ndigits);
+        if (carry)
+                r[ndigits - 1] &= (1ull << 63) - 1;
+        for (i = 1; carry || !vli_is_zero(q, ndigits); i++) {
+                u64 qc[ECC_MAX_DIGITS * 2];
+
+                vli_umult(qc, q, c2, ndigits);
+                if (carry)
+                        vli_uadd(qc, qc, mod[0], ndigits * 2);
+                vli_set(q, qc + ndigits, ndigits);
+                vli_clear(qc + ndigits, ndigits);
+                carry = vli_is_negative(qc, ndigits);
+                if (carry)
+                        qc[ndigits - 1] &= (1ull << 63) - 1;
+                if (i & 1)
+                        vli_sub(r, r, qc, ndigits * 2);
+                else
+                        vli_add(r, r, qc, ndigits * 2);
+        }
+        while (vli_is_negative(r, ndigits * 2))
+                vli_add(r, r, m, ndigits * 2);
+        while (vli_cmp(r, m, ndigits * 2) >= 0)
+                vli_sub(r, r, m, ndigits * 2);
+
+        vli_set(result, r, ndigits);
+}
+
+/*
+ * Computes result = product % mod, where product is 2N words long.
+ * Reference: Ken MacKay's micro-ecc.
+ * Currently only designed to work for curve_p or curve_n.
+ */
+static void vli_mmod_slow(u64 *result, u64 *product, const u64 *mod,
+                          unsigned int ndigits)
+{
+        u64 mod_m[2 * ECC_MAX_DIGITS];
+        u64 tmp[2 * ECC_MAX_DIGITS];
+        u64 *v[2] = { tmp, product };
+        u64 carry = 0;
+        unsigned int i;
+        /* Shift mod so its highest set bit is at the maximum position. */
+        int shift = (ndigits * 2 * 64) - vli_num_bits(mod, ndigits);
+        int word_shift = shift / 64;
+        int bit_shift = shift % 64;
+
+        vli_clear(mod_m, word_shift);
+        if (bit_shift > 0) {
+                for (i = 0; i < ndigits; ++i) {
+                        mod_m[word_shift + i] = (mod[i] << bit_shift) | carry;
+                        carry = mod[i] >> (64 - bit_shift);
+                }
+        } else
+                vli_set(mod_m + word_shift, mod, ndigits);
+
+        for (i = 1; shift >= 0; --shift) {
+                u64 borrow = 0;
+                unsigned int j;
+
+                for (j = 0; j < ndigits * 2; ++j) {
+                        u64 diff = v[i][j] - mod_m[j] - borrow;
+
+                        if (diff != v[i][j])
+                                borrow = (diff > v[i][j]);
+                        v[1 - i][j] = diff;
+                }
+                i = !(i ^ borrow); /* Swap the index if there was no borrow */
+                vli_rshift1(mod_m, ndigits);
+                mod_m[ndigits - 1] |= mod_m[ndigits] << (64 - 1);
+                vli_rshift1(mod_m + ndigits, ndigits);
+        }
+        vli_set(result, v[i], ndigits);
+}
+
+/* Computes result = product % mod using Barrett's reduction with precomputed
+ * value mu appended to the mod after ndigits, mu = (2^{2w} / mod) and have
+ * length ndigits + 1, where mu * (2^w - 1) should not overflow ndigits
+ * boundary.
+ *
+ * Reference:
+ * R. Brent, P. Zimmermann. Modern Computer Arithmetic. 2010.
+ * 2.4.1 Barrett's algorithm. Algorithm 2.5.
+ */
+static void vli_mmod_barrett(u64 *result, u64 *product, const u64 *mod,
+                             unsigned int ndigits)
+{
+        u64 q[ECC_MAX_DIGITS * 2];
+        u64 r[ECC_MAX_DIGITS * 2];
+        const u64 *mu = mod + ndigits;
+
+        vli_mult(q, product + ndigits, mu, ndigits);
+        if (mu[ndigits])
+                vli_add(q + ndigits, q + ndigits, product + ndigits, ndigits);
+        vli_mult(r, mod, q + ndigits, ndigits);
+        vli_sub(r, product, r, ndigits * 2);
+        while (!vli_is_zero(r + ndigits, ndigits) ||
+               vli_cmp(r, mod, ndigits) != -1) {
+                u64 carry;
+
+                carry = vli_sub(r, r, mod, ndigits);
+                vli_usub(r + ndigits, r + ndigits, carry, ndigits);
+        }
+        vli_set(result, r, ndigits);
+}
+
 /* Computes p_result = p_product % curve_p.
  * See algorithm 5 and 6 from
  * http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf
@@ -513,14 +775,33 @@ static void vli_mmod_fast_256(u64 *result, const u64 *product,
         }
 }
 
-/* Computes result = product % curve_prime
- *  from http://www.nsa.gov/ia/_files/nist-routines.pdf
-*/
+/* Computes result = product % curve_prime for different curve_primes.
+ *
+ * Note that curve_primes are distinguished just by heuristic check and
+ * not by complete conformance check.
+ */
 static bool vli_mmod_fast(u64 *result, u64 *product,
                           const u64 *curve_prime, unsigned int ndigits)
 {
         u64 tmp[2 * ECC_MAX_DIGITS];
 
+        /* Currently, both NIST primes have -1 in lowest qword. */
+        if (curve_prime[0] != -1ull) {
+                /* Try to handle Pseudo-Marsenne primes. */
+                if (curve_prime[ndigits - 1] == -1ull) {
+                        vli_mmod_special(result, product, curve_prime,
+                                         ndigits);
+                        return true;
+                } else if (curve_prime[ndigits - 1] == 1ull << 63 &&
+                           curve_prime[ndigits - 2] == 0) {
+                        vli_mmod_special2(result, product, curve_prime,
+                                          ndigits);
+                        return true;
+                }
+                vli_mmod_barrett(result, product, curve_prime, ndigits);
+                return true;
+        }
+
         switch (ndigits) {
         case 3:
                 vli_mmod_fast_192(result, product, curve_prime, tmp);
@@ -529,13 +810,26 @@ static bool vli_mmod_fast(u64 *result, u64 *product,
                 vli_mmod_fast_256(result, product, curve_prime, tmp);
                 break;
         default:
-                pr_err("unsupports digits size!\n");
+                pr_err_ratelimited("ecc: unsupported digits size!\n");
                 return false;
         }
 
         return true;
 }
 
+/* Computes result = (left * right) % mod.
+ * Assumes that mod is big enough curve order.
+ */
+void vli_mod_mult_slow(u64 *result, const u64 *left, const u64 *right,
+                       const u64 *mod, unsigned int ndigits)
+{
+        u64 product[ECC_MAX_DIGITS * 2];
+
+        vli_mult(product, left, right, ndigits);
+        vli_mmod_slow(result, product, mod, ndigits);
+}
+EXPORT_SYMBOL(vli_mod_mult_slow);
+
 /* Computes result = (left * right) % curve_prime. */
 static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right,
                               const u64 *curve_prime, unsigned int ndigits)
@@ -908,6 +1202,85 @@ static void ecc_point_mult(struct ecc_point *result,
         vli_set(result->y, ry[0], ndigits);
 }
 
+/* Computes R = P + Q mod p */
+static void ecc_point_add(const struct ecc_point *result,
+                   const struct ecc_point *p, const struct ecc_point *q,
+                   const struct ecc_curve *curve)
+{
+        u64 z[ECC_MAX_DIGITS];
+        u64 px[ECC_MAX_DIGITS];
+        u64 py[ECC_MAX_DIGITS];
+        unsigned int ndigits = curve->g.ndigits;
+
+        vli_set(result->x, q->x, ndigits);
+        vli_set(result->y, q->y, ndigits);
+        vli_mod_sub(z, result->x, p->x, curve->p, ndigits);
+        vli_set(px, p->x, ndigits);
+        vli_set(py, p->y, ndigits);
+        xycz_add(px, py, result->x, result->y, curve->p, ndigits);
+        vli_mod_inv(z, z, curve->p, ndigits);
+        apply_z(result->x, result->y, z, curve->p, ndigits);
+}
+
+/* Computes R = u1P + u2Q mod p using Shamir's trick.
+ * Based on: Kenneth MacKay's micro-ecc (2014).
+ */
+void ecc_point_mult_shamir(const struct ecc_point *result,
+                           const u64 *u1, const struct ecc_point *p,
+                           const u64 *u2, const struct ecc_point *q,
+                           const struct ecc_curve *curve)
+{
+        u64 z[ECC_MAX_DIGITS];
+        u64 sump[2][ECC_MAX_DIGITS];
+        u64 *rx = result->x;
+        u64 *ry = result->y;
+        unsigned int ndigits = curve->g.ndigits;
+        unsigned int num_bits;
+        struct ecc_point sum = ECC_POINT_INIT(sump[0], sump[1], ndigits);
+        const struct ecc_point *points[4];
+        const struct ecc_point *point;
+        unsigned int idx;
+        int i;
+
+        ecc_point_add(&sum, p, q, curve);
+        points[0] = NULL;
+        points[1] = p;
+        points[2] = q;
+        points[3] = &sum;
+
+        num_bits = max(vli_num_bits(u1, ndigits),
+                       vli_num_bits(u2, ndigits));
+        i = num_bits - 1;
+        idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1);
+        point = points[idx];
+
+        vli_set(rx, point->x, ndigits);
+        vli_set(ry, point->y, ndigits);
+        vli_clear(z + 1, ndigits - 1);
+        z[0] = 1;
+
+        for (--i; i >= 0; i--) {
+                ecc_point_double_jacobian(rx, ry, z, curve->p, ndigits);
+                idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1);
+                point = points[idx];
+                if (point) {
+                        u64 tx[ECC_MAX_DIGITS];
+                        u64 ty[ECC_MAX_DIGITS];
+                        u64 tz[ECC_MAX_DIGITS];
+
+                        vli_set(tx, point->x, ndigits);
+                        vli_set(ty, point->y, ndigits);
+                        apply_z(tx, ty, z, curve->p, ndigits);
+                        vli_mod_sub(tz, rx, tx, curve->p, ndigits);
+                        xycz_add(tx, ty, rx, ry, curve->p, ndigits);
+                        vli_mod_mult_fast(z, z, tz, curve->p, ndigits);
+                }
+        }
+        vli_mod_inv(z, z, curve->p, ndigits);
+        apply_z(rx, ry, z, curve->p, ndigits);
+}
+EXPORT_SYMBOL(ecc_point_mult_shamir);
+
 static inline void ecc_swap_digits(const u64 *in, u64 *out,
                                    unsigned int ndigits)
 {
@@ -1051,6 +1424,9 @@ int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve,
 {
         u64 yy[ECC_MAX_DIGITS], xxx[ECC_MAX_DIGITS], w[ECC_MAX_DIGITS];
 
+        if (WARN_ON(pk->ndigits != curve->g.ndigits))
+                return -EINVAL;
+
         /* Check 1: Verify key is not the zero point. */
         if (ecc_point_is_zero(pk))
                 return -EINVAL;